# Factoring formulas

Below are some factoring formulas that are used to factor some common math expressions

a2 - b2 = ( a - b ) × ( a + b )

a4 - b4 = ( a - b ) × ( a + b ) × ( a2 + b2 )

a6 - b6 = ( a - b ) × ( a + b ) × ( a2 - ab + b2 ) × ( a2 + ab + b2 )

a8 - b8 = ( a - b ) × ( a + b ) × ( a2 + b2 ) × ( a4 + b4 )

a3 + b3 = ( a + b ) × ( a2 - ab + b2 )

a3 - b3 = ( a - b ) × ( a2 + ab + b2 )

a5 - b5 = ( a - b ) × ( a4 + a3b + a2b2 + ab3 + b4 )

a5 + b5 = ( a + b ) × ( a4 - a3b + a2b2 - ab3 + b4 )

a6 - b6 = ( a - b ) × ( a5 + a4b + a3b2 + a2b3 + ab4 + b5 )

a6 + b6 = ( a2 + b2 ) × ( a4 - a2b2 + b4 )

a7 - b7 = ( a - b ) × ( a6 + a5b + a4b2 + a3b3 + a2b4 + ab5 + b6 )

a4 + a2b2 + b4 = ( a2 + ab + b2 )× ( a2 - ab + b2 )

a4 + 4b4 = ( a2 + 2ab + 2b2 )× ( a2 - 2ab + 2b2 )

Trick to factor an - bn when n is an odd number. You cannot use this trick if n is even or to factor an + bn

First start by writing ( a - b ) × ( ..................................................)

Then, fill in the parenthesis on the right

To do this, follow this guideline.

Subtract 1 from n. For example, if n = 7 as in a7 - b7, subtract 1 from 7 to get 6.

The first term is always going to be the first variable that is a raised to the power of 6

The first term is always going to be the second variable that is b raised to the power of 6

The operation inside is always a plus

So it is going to look like ( a - b ) × (a6 + .................................................. + b6)

Now here is the real tricky part

To get the next term, is a5b. This is done by subtracting 1 from 6 and incorporating the other variable

Now all you have to do is to keep subtracting 1 to the exponent of a and adding 1 to the exponent of b as shown below

The next term will be a4b2.

Do this until the variable a disappears and you will end up with the answer already shown above

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